thermal physics methods of heat transfer conduction convection radiation

1Thermal Physics

METHODS OF HEAT TRANSFER

CONDUCTION

CONVECTION

RADIATION

ptD_transfer.ppt

2

Overview of Thermal Physics Module:1. Thermodynamic Systems:

Work, Heat, Internal Energy0th, 1st and 2nd Law of Thermodynamics

2. Thermal Expansion

3. Heat Capacity, Latent Heat

4. Methods of Heat Transfer:Conduction, Convection, Radiation

5. Ideal Gases, Kinetic Theory Model

6. Second Law of ThermodynamicsEntropy and Disorder

7. Heat Engines, Refrigerators

3

METHODS OF HEAT TRANSFER energy transfer (heat, Q) due to a temperature difference, T

CONDUCTION CONVECTION RADIATION

§17.7 p591

system, T

Qnet

Environment, TE

European heat wave, 2003 ~35 000 deaths in France

References: University Physics 12th ed Young & Freedman

4

Live sheep tradeSunday, October 26, 2003

Sheep to shore ... finally

The Labor Opposition will pursue the Government over the cost of the "ship of death" saga, which ended on Friday when 50,000 Australian sheep at sea for three months began being unloading in Eritrea.

5Heat Conduction

Conduction is heat transfer by means of molecular agitation within a material without any motion of the material as a whole.

If one end of a metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones. TH

TC

conduction though glass

Q

Q

6

For conduction between two plane surfaces (eg heat loss through the wall of a house) the rate of heat transfer is

energy transferred

through slabQ

THTC

L

H CQ T Tk A

t L

dQ dTk A

dt dx

Thermal conductivity k (W.m-1.K-1)

steady-state

heat current H = dQ/dt

Q QA

7

H CQ T Tk A

t L

dQ dTk A

dt dx

steady-state

Thermal Conduction through a uniform slab

0 xLTC

TH

temperature gradientdT

dx

8Material Thermal conductivity

k (W.m-1.K-1)

diamond 2450

Cu 385

Al 205

Brick 0.2

Glass 0.8

Body fat 0.2

Water 0.6

Wood 0.2

Styrofoam 0.01

Air 0.024

Thermal conductivity, k property of the material

kdiamond very high: perfect heat sink, e.g. for high power laser diodes

khuman low: core temp relatively constant (37 oC)

kair very low: good insulator * home insulation * woolen clothing * windows double glazing Metals – good conductors: electrons transfer energy from hot to cold

9Heat Convection

Convection is heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it.

Convection above a hot surface occurs because hot air expands, becomes less dense and rises (natural or free). Convection assisted by breeze, pump or fan – forced convection.

Hot water is likewise less dense than cold water and rises, causing convection currents which transport energy.

Convection coefficient, hT between surface and air way from surface2 1~ ( )

dQh A T T

dt

10

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html

11

Sea & Land Breezes, Monsoons

http://sol.sci.uop.edu/~jfalward/heattransfer/heattransfer.html

35 oC 20 oC 17 oC11 oC

What is the role of heat capacity, c of water and soil?

12RADIATION Energy transferred by electromagnetic waves

All materials radiate thermal energy in amounts determined by their temperature, where the energy is carried by photons of light in the infrared and visible portions of the electromagnetic spectrum.

Thermal radiation wavelength ranges: IR ~ 100 - 0. 8 mVisible ~ 0.8 - 0.4 m 800 – 400 nmUV ~0.4 - 0.1 m

For exam: more detail than in the textbook

13Ludwig Boltzmann (1844-1906)

All objects above absolute zero emit radiant energy and the rate of emission increases and the peak wavelength decreases as the temperature of object increases

14

Thermography

15

Power absorbed by surface of an object

A, a

Qabs4abs

abs s

dQP Aa T

dt

Ts

Absorption & Stefan-Boltzmann Law

Incident radiation (INTENSITY I - energy passing through a square metre every second

Iinc = P / A Iabs = a Iinc

• Surface Area, A• Absorption coefficient, a = 0 to 1• Stefan-Boltzmann constant

σ = 5.67 x 10-8 W.m-2.K-4

16

Power radiated from the surface of an object

A, e, T Qrad4rad

rad

dQP Ae T

dt

net rad absPP P

Emission & Stefan-Boltzmann Law

Pnet > 0 net heat transfer out of system

• Surface Area, A• Emissivity, e = 0 to 1• Stefan-Boltzmann constant

σ = 5.67 x 10-8 W.m-2.K-4

17

A blackbody absorbs all the radiation incident upon it and emits the max possible radiation at all wavelengths (e = a = 1)

A graybody is a surface that absorbs a certain proportion of the energy of a blackbody, the constant being constant over the entire band of wavelengths(0 e = a < 1)

emissivity e

absorption coefficient (absorptivity) a

Stefan-Boltzmann constant = 5.6710-8 W.m-2.K-4

18Wien’s Displacement Law

peak

b

T

Wien constant

b = 2.89810-3 m.K

Blackbody: absorbs ALL the EMR radiation falling on it & emits the max possible energy over all wavelengths

19 Wien’s Displacement Law

peak

b

T

Wien constant:

b = 2.89810-3 m.K

Blackbody radiation curves show differentpeak wavelengths at various temperatures

20Stefan-Boltzmann constant, = 5.67 x 10-8 W.m-2.K-4

* emissivity, e = 0 to 1 Blackbody, e = 1* Absorption coefficient, a = 0 to 1 * At a temperature T a = e all wavelengths* T > 700 oC visible radiation (dull red ~ 800 oC white ~ 2000 oC)* Black surface (e ~ 1) – good emitter / absorber* Polished surface (e ~ 0.01) – poor emitter / absorber, good reflector * Hot stars – blue* Cool stars - red

Water (e ~ 0.96) Earth (e ~ 0.3)

21

Sun (6000 K - hot!) Earth (300 K - cold!)

Visible radiation Infrared radiation

22

Sun & Photosynthesis

TSun ~ 6000 K

peak ~ 480 nm (blue/green)

UV (ionization of molecules) ~ 9%

Visible (excite molecules) ~ 49 %

IR (warm) ~ 42%

0.1% of radiant energy captured by chlorophyll of plants

What about life on Earth if the Sun was hotter or colder ?

23

Emissivity, e – the nature of the surface

e ~ 0.8 e ~ 0.4

Summer clothing: white reflects radiant energy better than black.

Wrap an ice-cube in black cloth and another in aluminium foil and place both in the sunshine. What will happen?

Why is the pupil of the eye black?


24Problem D1: Estimate the Sun’s temperature

Assume e = 1Distance from Sun to Earth: RSE = 1.5 x 1011 m Radius of the Sun: RS = 6.9 x 108 mSolar radiation at Earth’s surface: I = 103 W.m-2

= 5.67 x 10-8 W.m-2.K-4

SolutionPower radiated by Sun

Prad = I A = I 4RSE2 = (103)(4)(1.5x1011)2 W = 2.83 x 1026 W

Surface area of the Sun, ASun = 4RS2 = 5.98 x 1018 m2

T 4 = Prad / (ASun e ) T = 5.4 x 103 K

RSE

RS

4radP Ae T

25Problem D.2 Estimate the Earth’s surface Temperature TE

(assume NO atmosphere)Solar constant Io= 1360 W.m-2

AE = 4RE2

Pabs = Prad TE = 255 K = -18 oCe = 1

Earth

Earth albedo (reflectivity) = 0.3

Adisk = RE2

What is natural greenhouse effect?

Power absorbed by Earth:Pabs = (1-) AdiskIo

Power radiated by Earth:Prad = AE TE

4

RSE

radiation emitted fromthe surface of a sphere

26

Earth’s albedo (reflectivity) = 0.3

Greenhouse Effect

27

American Journal of Physics: Feb 1983

28

Selective surfacesEmissivity, e – the nature of the surface

Value of e is temperature and wavelength dependent

0

1e

short long

Selective surface used in solar collectors

Good emitter / absorber at short wavelengths

Poor emitter / absorber at long wavelengths

29

0

1

e

0

1

e

Black paint

White paint

Black skin

White skin

Black skin absorbs heat more readily than white skin but also radiates heat more readily - the heat balance favours black skin in the tropics

short longshort long

30Problem D.3

Steel plates are placed on a non-conducting opaque surface, normal to incident solar radiation (direct + diffuse) of750 W.m-2.

Neglecting convection, calculate the equilibrium temperature T for a polished steel plate (e = 0.07) and a dull steel plate (e = 0.8). Assume graybody behaviour.

Calculate the effect of coating a steel plate with a selective surface

e = 0.92 < 2 m e = 0.10 > 2 mshort long

31

SolutionIdentify / Setup

Pabs = a I A I = 750 W.m-2

e = a Equilibrium: Pabs = Prad

Execute

4radP Ae T

4

0.25

o339 K = 66 C

a I A e I A Ae T

IT

T

The equilibrium temperature is the same for both surfaces – the equilibrium temperature is unaffected by the area and nature of the surface if the emissivity (and absorptivity) remain constant over the range of temperature & wavelength.

32Assume Sun a blackbody at 5800 K

Absorbed: virtually all the incident radiation lies at < 2 m thus

Pabs = e I A = (0.92)(750)A = 690

Radiated: most of the radiation will be at wavelengths > 2 µm

Prad = e A T4 = 0.1 A T4

Equil Pabs = Prad

T = 591 K = 317 oC 250 oC hotter

e

2 m

0.10

0.92short long

33

Problem D.4Semester 1, 2007 Examination

An igloo is a hemispherical enclosure built of ice. Elmo’s igloo has an inner radius of 2.55 mm and the thickness of the ice is 0.30 m. This thickness can be considered small compared to the radius. Heat leaks out of the igloo at a rate determined by the thermal conductivity of ice, kice = 1.67 W.m-1.K-1.

At what rate must thermal energy be generated inside the igloo to maintain a steady air temperature inside the igloo at 6.5 oC when the outside temperture is -40 oC?

Ignore all thermal energy losses by conduction through the ground, or any heat transfer by radiation or convection or leaks.

34SolutionIdentify / Setup

thickness t = 0.30 m

radius r = 2.55 m

kice = 1.67 W.m-1.K-1

dQ dTk A

dt dx

The rate of energy production must be equal to the rate of loss of thermal energy by conduction through the hemispherical ice wall.

Rate of energy transfer by conduction

6.5 oC

-40 oC

35

dQ/dt = ? W

k = 1.67 W.m-1.K-1

dT = {6.5 – (– 40)} oC = 46.5 oC

thickness of ice, dx = 0.30 m

area, A = surface area of hemisphere = (4 R2) / 2 = 2 R2

Because the thickness of the ice is much smaller than either the inside or outside radius, it does not matter which radius is used – taking the average radius

R = (2.55 + 0.15) m = 2.70 m

36Execute

dQ/dt = – (1.67)(2)(2.70)2(46.5)/0.30 W

dQ/dt = – 1.2 104 W

dQ dTk A

dt dx

Evaluate

sensible valueunitssignificant figuresdid I answer the question ?

37

Problem D.5

Suppose a human could live for 120 min unclothed in air at 8 oC.

How long could they live in water at 8 oC?

38Problem D.5Suppose a human could live for 120 min unclothed in air at 8 oC. How long could they live in water at 8 oC?

Solution

Identify / Setup

Thermal conductivities kair = 0.024 W.m-1.K-1 kwater = 0.6 W.m-1.K-1

Execute

Evaluate

&

0.024(120) min 4.8 min

0.6

W AW A

W A AW A

A W W

Q T Q T Q Tk A k A k A

t x t x t x

t k kt t

t k k

39

Why do droplets of water dance over the very hot pan ?


Problem D.6

40

Why do droplets of water dance over the very hot pan ?


Water at the bottom of the drops is evaporated and provides insulation against further evaporation.

41

Problem D.7

An aluminium pot contains water that is kept steadily boiling (100 ºC). The

bottom surface of the pot, which is 12 mm thick and 1.5104 mm2 in area,

is maintained at a temperature of 102 °C by an electric heating unit. Find

the rate at which heat is transferred through the bottom surface. Compare

this with a copper based pot. The thermal conductivities for aluminium and

copper are

kAl = 235 W.m-1.K-1 and kCu = 401 W.m-1.K-1

42

SolutionIdentify / Setup

TH = 102 oC

TC = 100 oC

Base area A = 1.5x104 mm2 = 1.5x10-2 m2

Base thickness L = 12 mm = 12x10-3 m

kAl = 235 W.m-1.K-1

kCu = 401 W.m-1.K-1

dT/dx = (TH – TC) / L

dQ/dt = ? W

dQ dTk A

dt dx

Execute

Al, dQ/dt = 5.9x102 W

Cu, dQ/dt = 1.0x103 W

Cu pots ~ 2 times more efficient

43“Body Heat”

Heat lost by convection is very important for humansFor a naked person, h ~ 7.1 W.m-2.K-1

Assume the person’s surface area is 1.5 m2, skin temperature of 33 oC and surrounding temperature 29 oC.

A = 1.5 m2 T = 33 oC TE = 29 oC

dQ/dtconvection = h A T = (7.1)(1.5)(4) W = 43 W

If there is a breeze, convection losses are greater – wind chill factorViscosity of fluids slows natural convection near a stationary surface by producing a boundary layer which has about the same insulating values of 10 mm plywood.

44For the naked person, estimate the net rate of energy radiated. = 1.5 m2 T = 33 oC = (33 + 273) K = 306 KTE = (29 + 273) K = 302 K assume e = 1 = 5.67x10-8 W.m-2.K-4

Pradiation = e A (T 4 – TE4) = 39 W

dQ/dtloss = dQ/dtradiation + dQ/dtconvection = 39 W + 43 W = 82 W

Ans. similar to the rate at which heat is generated by the

body when resting

45

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html

Why not heat the water at the top?

CONVECTION

46


Warm air rises above the ground

Forced convection

CONVECTION

47

Why do we get this pollution haze?

Temperature inversion prevents air rising and the dispersing the pollution


CONVECTION

48

Why are the cooling coils at the top ?

In bathrooms, the heater is often near the ceiling. Problem ?


CONVECTION

49

peak ff b T

Wien constant

bf = 2.83 kB/h s-1.K

RADIATION

50

Why are pipes in solar panels painted black ?


RADIATION

51

Highly reflecting metal foil keepsinside temperature low.

RADIATION


52

Lemur at the right is activeduring the day; it pointsits belly toward the sun oncold mornings.

Lemur at left is nocturnal,so the dark fur poses nodisadvantage in absorbingexcessive sunlight.


RADIATION

53Think about

* Two different materials at the same temperature have different emissivities. Which one glows the brightest?

* Why are fireplace pokers made of iron and not copper?

* Some animals have hair which is composed of solid tubular strands, while others have hollow, air-filled tubes. Where would one more likely find the latter animal: In cold climates, or warm?

* Steel reinforcement bars add stability to concrete walls. Do they also enhance the insulating value of concrete?

* Wind chill factor

* Drapes hung close to a cold window

54

* Clothing

* Should you lower the blinds and draw the curtains on a hot day? * When one steps from a shower on a cold morning, why does the tile floor seem so much colder than the air?

* Place a wooden spoon and a metal spoon in the freezer. Which will cool faster? After several hours, what would they feel like?

* Why do people become "flushed" when overheated?

thermal physics methods of heat transfer conduction convection radiation

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